Question

1 + cosA/1 - cosA = (cosecA + cotA)²​

Answer 1

=> (1-cosA/1+cosA)

=> (1-cosA/1+cosA)*(1-cosA/1-cosA)

=> (1-cosA)² / (1-cos²A)

=> (1-cosA)² / sin²A

=> (1-cosA)²/(sinA)²

=> (1-cosA/sinA)²

=> (cosecA - cotA)²

Answer 2

Answer:

$\frac{1 + cos(a )}{1 - cos(a)} \times \frac{1 + cos(a)}{1 + cos(a)}$

Step-by-step explanation:

$\frac{(1 + cos(a))^2}{1 - {cos}^{2}a }$

$\frac{(1 + cos(a))^2}{ {sin}^{2}a }$

${( \frac{1 + cos(a)}{sin(a)} )}^{2}$

$( \frac{1}{sin(a)} + \frac{cos(a)}{sin(a)} )^{2}$

$(cosec(a) + cot(a)) ^{2}$

Hence it is proved.